Solution of the boundary value problem for the integrable discrete SRS system on the semi-line

The complete solution of the initial-boundary value problem for the integra ble discrete version of the stimulated Raman scattering system on the semi- line is constructed by means of the inverse spectral transform. The spectra l data obey a Riccati time evolution equation which allows for soliton gene ration out of a medium initially at rest. It is also proved that the constr uction of the solution at any finite distance actually results in solving a n algebraic system.